There exist in the art many schemes for assigning work to a processor of a multiprocessor computer system where the goal is the highest utilization of the processors. In situations where the features of each processor are identical this problem of assigning work is rather straightforward and simple schemes based solely on the importance of the work (priority) perform well. Additionally, in this symmetric multiprocessor environment, schemes of decentralized assignment (where each processor is responsible for assigning its own work) can perform well. But in the case of asymmetric multiprocessors the assignment of work is much more complex. This complexity is caused by the fact that a given processor may be unable to execute a given work unit because of that work unit's need for a feature not present on the given processor. This situation is further exacerbated when the features required by a work unit dynamically change during execution, or if the processors may have their feature availability changed during operation, or even if the configuration of processors changes during operation. There are schemes, in the prior art, which do consider asymmetric multiprocessors when scheduling work units, but they tend to limit their schemes to only direct assignment. That is, when a processor becomes available for work these schemes will only choose ready work which is capable of executing on the available processor. If there is no ready work that can execute on the available processor, the available processor will remain idle, even though there may be some currently executing work which could be moved (redirected) to the available processor to be replaced by a ready piece of work. There are also some examples in the prior art, (for example U.S. Pat. No. 4,394,727 dated Jul. 19, 1983, Multiprocessor Task Dispatching Apparatus, by Roy L. Hoffman et al, assigned to the assignee of the present invention) where work will be moved on occasion, but only if the work replacing it is of a higher priority, thereby still leaving idle processors much of the time. In the prior art problems involving asymmetric assignments were thought to be too complex to solve efficiently or with adequate performance benefit to warrant the overhead of processing the movement of work between processors.